To find the measures of the angles in the triangle, we utilize the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
Given the angle measures:
- \( (5x - 1)^\circ \)
- \( (8x + 5)^\circ \)
- \( (4x + 6)^\circ \)
We can write the equation representing the sum of the angles:
\[ (5x - 1) + (8x + 5) + (4x + 6) = 180 \]
Now, combining like terms gives us:
\[ 5x + 8x + 4x - 1 + 5 + 6 = 180 \]
\[ 17x + 10 = 180 \]
Next, we isolate \( x \):
\[ 17x = 180 - 10 \] \[ 17x = 170 \] \[ x = \frac{170}{17} = 10 \]
Now that we have \( x \), we can find each angle:
- For the first angle \( (5x - 1)^\circ \):
\[ 5(10) - 1 = 50 - 1 = 49^\circ \]
- For the second angle \( (8x + 5)^\circ \):
\[ 8(10) + 5 = 80 + 5 = 85^\circ \]
- For the third angle \( (4x + 6)^\circ \):
\[ 4(10) + 6 = 40 + 6 = 46^\circ \]
Now we have the measures of the angles:
- First angle: \( 49^\circ \)
- Second angle: \( 85^\circ \)
- Third angle: \( 46^\circ \)
Thus, the angles of the triangle are:
49°, 46°, and 85°
Checking the provided responses, the correct one is:
46°, 49°, and 85°.